New operations for informative combination of two partial order relations with illustrations on pollution data

Area of Science:

• Decision Analysis
• Operations Research
• Data Science

Background:

• Ranking objects with multiple criteria often requires complex weighting schemes.
• Partial order relations offer an alternative when direct scoring is infeasible.
• Existing methods may not adequately handle combining information from disparate sources.

Purpose of the Study:

• To present methods for constructing and processing partial order relations (posets) for multi-criteria ranking.
• To investigate techniques for combining information from two sources, considering equal importance and prioritized scenarios.
• To illustrate the application of these methods using real-world pollution data.

Main Methods:

• Developing algorithms for generating and manipulating partial order relations.
• Implementing methods for merging information from multiple criteria sources into a unified poset.
• Applying techniques for ranking objects based on derived partial orders, including prioritized source integration.

Main Results:

• Demonstrated the feasibility of ranking objects using partial orders without explicit weighting.
• Showcased effective strategies for combining information from two sources, accommodating different importance levels.
• Successfully applied the methodology to pollution data from 59 regions, yielding meaningful rankings.

Conclusions:

• Partial order relations provide a valuable framework for multi-criteria decision-making, especially when weighting is problematic.
• The proposed methods offer a flexible and robust approach to integrating information from multiple sources for object ranking.
• The application to pollution data highlights the practical utility of poset-based ranking in environmental analysis.